"It is not a good thing," party general secretary Madhusudan Mistry told reporters, questioning the two leaders issuing statements to the media on the issues when the Congress chief and vice president are "easily accessible" to them.
The AICC briefing also saw spokesperson Abhishek Singhvi dubbing as "not appropriate" the statements of Singh.
Digvijay Singh had remarked that Rahul Gandhi's silence on critical issues had contributed to their loss in the "war of perception". He had said the party vice-president should be "more visible and heard more" to bring the Congress back on the path of revival.
The AICC has already distanced the party from Dwivedi's remarks that leaders of 65 to 70 years of age should not take up active posts in the organisation.
Singhvi also did not take kindly to the remarks of Maharashtra Chief Minister Prithviraj Chavan that Rahul Gandhi's reluctance to join the Union Cabinet cost the party.
He wondered as to what was new as the then Prime Minister Manmohan Singh had time and again requested Gandhi to become a Minister. "It is an old and known view".
The remarks of Mistry, who is considered close to the Congress Vice President as well as Singhvi, show disapproval by the leadership of the remarks by Singh and Dwivedi, who have been senior general secretaries in the party.
Responding to a volley of questions over Digvijay Singh's remarks, Singhvi said, "This may be his personal view. But this is certainly not the time to advise each other through the media rather than focussing on strengthening the party by working collectively.... It is not appropriate".
Echoing a similar view, Mistry questioned Singh and Dwivedi for their going to the press over internal party matters.
"Those who have easy accessibility to Congress President and Congress Vice President and who were and are party to the decision making process regarding elections and who express their concerns without any fear...then why should they go to the press to tell all this.
"They can meet the top leaders and tell them directly. Matter ends there. Telling media does not solve problems", Mistry said.
Taking a dig at Dwivedi, he said that it is the "prerogative" of the party chief whether an office bearer should be of sixty years of age or forty and therefore it should be nobody's business to suggest that one should retire after a certian age.
Besides age, there are various other factors like performance and experience to decide on the issue of office bearers. "I fail to understand that as to why those who have been involved in the whole process are going public", he wondered.
The development is significant given the fact that a reshuffle of the AICC is on the cards in the wake of the Lok Sabha poll debacle.